2 Answers
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The gauge of wire depends on the strength of the branch you want to train. Give the branch a bit of a bit or bend and note how much force you need, then bend the wire you have. If it takes more force to bend the wire than the branch you have the right gauge wire.

Branch > Wire = Bad
Branch < Wire = Good

If you can bend the wire with less force than the branch, you can "double wire" the branch.

If you have branches that you want to go down anything more than a slight bend, there are better techniques than wiring and bending the branch. These techniques are for when you want significant or dramatic drops in your branches.

The most basic technique is to have a wire wrapped around the branch and then anchored at a lower point. This could either be somewhere on the pot, a protruding root or the bade of the trunk. Make sure the wire is tort. As time goes by you can reanchor to tighten the wire. There are also devices which have use screw that can be used to tighten the wire over time.

For areas where the wire wraps around a branch you can place a piece of cloth or folder paper to prevent the wire biting into the tree.

Similar to the above technique you can use weights to weigh down branches. This is helpful in cases where wiring a branch is not useful due to the thickness of the branch.

The next technique can be used in combination with either wiring or anchoring. Select the area of the branch where the bend and pressure would be greatest. At this area, using a very sharp knife and take off the top layers from the branch. You shouldn't dig down further than 40% of the thickness of the branch and the shape you are cutting should be a rectangle. The area of the rectangle should be minimised to only the area necessary. Don't wire over this area and cover it with tape to prevent infection.

Another advanced technique is best practiced several times on plants that you aren't worried about losing a branch or two. This involves physically snapping the branches. I've seen this also covered in bonsai books where for thicker branches they use a hammer to bash it until it breaks. This snapping or bashing should only be done from one side and avoid ripping or snapping so far that the branch snaps clean off.

Once the snapping is done, the branch should be bandaged at the area of the break until there are signs of growth and confirmation the branch has survived. Then the wound can be tidied with as sharp knife.

These techniques should be researched further as there are more detailed explanations available with diagrams and images if you don't want to go for trial and error. This is just an intro to some of the techniques available.